Let F(x)=x^2 And G(x)=2x+5 And H(x)= X^2-1 Find F [g (x-1) ] - Wyzant

Subject ZIP Search Search Find an Online Tutor Now Ask Ask a Question For Free Login Math Algebra 2 let f(x)=x^2 and g(x)=2x+5 and h(x)= x^2-1 Find f [g (x-1) ] Follow • 1 Comment • 1 More Report Report

09/07/20

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So for these types of questions I like to work from the inside out (starting with the inside function, then moving to the outside function. For each function, we replace x with whatever is inside the parenthesis.

1) We start with g(x-1): We replace x in the function g(x) with x - 1. So g(x - 1) = 2(x - 1) + 5

2) Now we move onto the outer function f(g(x - 1): For this we take the function f(x) = x2 and replace x with g(x - 1). So f(g(x - 1)) = (g(x - 1))2

3) Finally, we plug in our function for g(x-1) from step 1 into our function for f(g(x-1)) from part 2.

So f(g(x - 1)) = (2(x - 1) +5)2

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I prefer to work from the inside out.

g(x) = 2x + 5

g(x - 1) = 2(x - 1) + 5 = 2x - 2 + 5 = 2x + 3

f(x) = x2

f(g(x - 1)) = f(2x + 3) = (2x + 3)2 = 4x2 + 12x + 9

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f(g(x)) = (2x + 5)2

f(g(x + 1) = (2(x + 1) + 5)2

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