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Kipish [7]
3 years ago
12

Please. Answer Fast! Use composition to determine if G(x) or H(x) is the inverse of F(x) for the

Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
3 0

Answer:

A. H(x) is an inverse of F(x)

Step-by-step explanation:

The given functions are:

F(x)=\sqrt{x-2}

G(x)=(x-2)^2

H(x)=x^2+2

We compose F(x) and G(x) to get:

(F\circ G)(x)=F(G(x))

(F\circ G)(x)=F((x-2)^2)

(F\circ G)(x)=\sqrt{(x-2)^2-2}

(F\circ G)(x)=\sqrt{x^2-4x+4-2}

(F\circ G)(x)=\sqrt{x^2-4x+2}

(F\circ G)(x)\ne x

Hence G(x) is not an inverse of F(x).

We now compose H(x) and G(x).

(F\circ H)(x)=F(H(x))

(F\circ H)(x)=F(x^2+2)

(F\circ H)(x)=\sqrt{x^2+2-2}

We simplify to get:

(F\circ H)(x)=\sqrt{x^2}

(F\circ H)(x)=x

Since (F\circ H)(x)=x, H(x) is an inverse of F(x)

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