Home > Precalculus > Function Composition

How do you find the (f o g o h) (x) for #f(x)=(x-2)/(2x+1), #g(x)=3x+1#, #h(x)=x^2#?

Answer 1

To find (f o g o h)(x) for the given functions ( f(x) = \frac{x-2}{2x+1} ), ( g(x) = 3x+1 ), and ( h(x) = x^2 ), follow these steps:

First, find ( (f o g)(x) ) by substituting ( g(x) ) into ( f(x) ): ( f(g(x)) = f(3x+1) = \frac{(3x+1)-2}{2(3x+1)+1} )
Next, find ( (f o g o h)(x) ) by substituting ( h(x) ) into ( f(g(x)) ): ( (f o g o h)(x) = f(g(h(x))) = f(g(x^2)) = \frac{(3x^2+1)-2}{2(3x^2+1)+1} )

Simplify the expression to get the final answer.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Sadie Ackerman

In this problem, ƒ o g o h = ƒ(g(h(x)))

Start out by plugging h into g.

ƒ(g(#x^2#)))

=ƒ(3(#x^2#) + 1)

= ƒ(#3x^2# + 1) Next, plug in the new function into ƒ.

= #(3x^2 + 1 - 2) / (2(3x^2 + 1) + 1)#

= #(3x^2 - 1) / (6x^2 + 3)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.