let f(x)=x^2 and g(x)=2x+5 and h(x)= x^2-1 Find f [g (x-1) ]

Answer 1

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

Answer 2

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

Answer 3

f(g(x)) = (2x + 5)²

f(g(x + 1) = (2(x + 1) + 5)²