Algebra InputsTrigonometry InputsCalculus InputsMatrix Inputs Basic algebra trigonometry calculus statistics matrices CharactersSolve for f \left\{\begin{matrix}\\f=\frac{x+gy+2g-4}{2}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.View solution stepsSteps for Solving Linear Equation f ( x ) = 3 x - 1 y g ( x ) = x ^ { 2 } - x - 2 \quad ( f - g ) ( x ) Swap sides so that all variable terms are on the left hand side. x^{2}-x-2\left(f-g\right)x=3x-ygx Use the distributive property to multiply -2 by f-g. x^{2}-x+\left(-2f+2g\right)x=3x-ygx Use the distributive property to multiply -2f+2g by x. x^{2}-x-2fx+2gx=3x-ygx Subtract x^{2} from both sides. -x-2fx+2gx=3x-ygx-x^{2} Add x to both sides. -2fx+2gx=3x-ygx-x^{2}+x Combine 3x and x to get 4x. -2fx+2gx=4x-ygx-x^{2} Subtract 2gx from both sides. -2fx=4x-ygx-x^{2}-2gx The equation is in standard form. \left(-2x\right)f=4x-2gx-gxy-x^{2} Divide both sides by -2x. \frac{\left(-2x\right)f}{-2x}=\frac{x\left(4-2g-gy-x\right)}{-2x} Dividing by -2x undoes the multiplication by -2x. f=\frac{x\left(4-2g-gy-x\right)}{-2x} Divide x\left(4-yg-x-2g\right) by -2x. f=\frac{gy}{2}+\frac{x}{2}+g-2 Solve for g \left\{\begin{matrix}g=\frac{4+2f-x}{y+2}\text{, }&y\neq -2\\g\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=2f+4\text{ and }y=-2\right)\end{matrix}\right.View solution stepsSteps for Solving Linear Equation f ( x ) = 3 x - 1 y g ( x ) = x ^ { 2 } - x - 2 \quad ( f - g ) ( x ) Add 2\left(f-g\right)x to both sides. 3x-ygx+2\left(f-g\right)x=x^{2}-x Use the distributive property to multiply 2 by f-g. 3x-ygx+\left(2f-2g\right)x=x^{2}-x Use the distributive property to multiply 2f-2g by x. 3x-ygx+2fx-2gx=x^{2}-x Subtract 3x from both sides. -ygx+2fx-2gx=x^{2}-x-3x Combine -x and -3x to get -4x. -ygx+2fx-2gx=x^{2}-4x Subtract 2fx from both sides. -ygx-2gx=x^{2}-4x-2fx Combine all terms containing g. \left(-yx-2x\right)g=x^{2}-4x-2fx The equation is in standard form. \left(-xy-2x\right)g=x^{2}-2fx-4x Divide both sides by -yx-2x. \frac{\left(-xy-2x\right)g}{-xy-2x}=\frac{x\left(x-2f-4\right)}{-xy-2x} Dividing by -yx-2x undoes the multiplication by -yx-2x. g=\frac{x\left(x-2f-4\right)}{-xy-2x} Divide x\left(-4+x-2f\right) by -yx-2x. g=-\frac{x-2f-4}{y+2} GraphQuizLinear Equation5 problems similar to: f ( x ) = 3 x - 1 y g ( x ) = x ^ { 2 } - x - 2 \quad ( f - g ) ( x )
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CopyCopied to clipboardx^{2}-x-2\left(f-g\right)x=3x-ygx Swap sides so that all variable terms are on the left hand side.x^{2}-x+\left(-2f+2g\right)x=3x-ygx Use the distributive property to multiply -2 by f-g.x^{2}-x-2fx+2gx=3x-ygx Use the distributive property to multiply -2f+2g by x.-x-2fx+2gx=3x-ygx-x^{2} Subtract x^{2} from both sides.-2fx+2gx=3x-ygx-x^{2}+x Add x to both sides.-2fx+2gx=4x-ygx-x^{2} Combine 3x and x to get 4x.-2fx=4x-ygx-x^{2}-2gx Subtract 2gx from both sides.\left(-2x\right)f=4x-2gx-gxy-x^{2} The equation is in standard form.\frac{\left(-2x\right)f}{-2x}=\frac{x\left(4-2g-gy-x\right)}{-2x} Divide both sides by -2x.f=\frac{x\left(4-2g-gy-x\right)}{-2x} Dividing by -2x undoes the multiplication by -2x.f=\frac{gy}{2}+\frac{x}{2}+g-2 Divide x\left(4-yg-x-2g\right) by -2x.3x-ygx+2\left(f-g\right)x=x^{2}-x Add 2\left(f-g\right)x to both sides.3x-ygx+\left(2f-2g\right)x=x^{2}-x Use the distributive property to multiply 2 by f-g.3x-ygx+2fx-2gx=x^{2}-x Use the distributive property to multiply 2f-2g by x.-ygx+2fx-2gx=x^{2}-x-3x Subtract 3x from both sides.-ygx+2fx-2gx=x^{2}-4x Combine -x and -3x to get -4x.-ygx-2gx=x^{2}-4x-2fx Subtract 2fx from both sides.\left(-yx-2x\right)g=x^{2}-4x-2fx Combine all terms containing g.\left(-xy-2x\right)g=x^{2}-2fx-4x The equation is in standard form.\frac{\left(-xy-2x\right)g}{-xy-2x}=\frac{x\left(x-2f-4\right)}{-xy-2x} Divide both sides by -yx-2x.g=\frac{x\left(x-2f-4\right)}{-xy-2x} Dividing by -yx-2x undoes the multiplication by -yx-2x.g=-\frac{x-2f-4}{y+2} Divide x\left(-4+x-2f\right) by -yx-2x.
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Quadratic equation { x } ^ { 2 } - 4 x - 5 = 0Trigonometry 4 \sin \theta \cos \theta = 2 \sin \thetaLinear equation y = 3x + 4Arithmetic 699 * 533Matrix \left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]Simultaneous equation \left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.Differentiation \frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }Integration \int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d xLimits \lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}Back to top
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View solution stepsSteps for Solving Linear Equation f ( x ) = 3 x - 1 y g ( x ) = x ^ { 2 } - x - 2 \quad ( f - g ) ( x ) Swap sides so that all variable terms are on the left hand side. x^{2}-x-2\left(f-g\right)x=3x-ygx Use the distributive property to multiply -2 by f-g. x^{2}-x+\left(-2f+2g\right)x=3x-ygx Use the distributive property to multiply -2f+2g by x. x^{2}-x-2fx+2gx=3x-ygx Subtract x^{2} from both sides. -x-2fx+2gx=3x-ygx-x^{2} Add x to both sides. -2fx+2gx=3x-ygx-x^{2}+x Combine 3x and x to get 4x. -2fx+2gx=4x-ygx-x^{2} Subtract 2gx from both sides. -2fx=4x-ygx-x^{2}-2gx The equation is in standard form. \left(-2x\right)f=4x-2gx-gxy-x^{2} Divide both sides by -2x. \frac{\left(-2x\right)f}{-2x}=\frac{x\left(4-2g-gy-x\right)}{-2x} Dividing by -2x undoes the multiplication by -2x. f=\frac{x\left(4-2g-gy-x\right)}{-2x} Divide x\left(4-yg-x-2g\right) by -2x. f=\frac{gy}{2}+\frac{x}{2}+g-2 Solve for g \left\{\begin{matrix}g=\frac{4+2f-x}{y+2}\text{, }&y\neq -2\\g\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=2f+4\text{ and }y=-2\right)\end{matrix}\right.
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