Question

If h(x) = x – 7 and g(x) = x2, which expression is equivalent to (g circle h) (5)?
(5 – 7)2
(5)2 – 7
(5)2(5 – 7)
(5 – 7)x2

Answer 1

Answer:

The equivalent expression to $(g{\circ}h)(5)$ is $(5-7)^{2}$ .

Explanation:

We have,

$h(x)=x-7\\g(x)=x^{2}$

We have to find the value of $(g{\circ}h)(5)$ .

In order to do so, let us first find the expression for $(g{\circ}h)$ ,

$(g{\circ}h)=g(h(x))$

Substituting the function $h(x)$ ,

$(g{\circ}h)=g(x-7)\\=(x-7)^{2}$

Let us now determine the value for $x=5$ ,

$(g{\circ}h)(5)=(5-7)^{2}$

Answer 2

We need to recall the following definitions to solve problem

The composition of functions f(x) and g(x) where g(x) is acting first is represented by f(g(x)) or (f ∘ g)(x)

This problem is about function.

Given h(x) = x – 7 and g(x) =$x^{2}$

We have to equivalent to (g ∘ h) (5)

First find the value of (g ∘ h) (x)

By the defination of composition of functions

(g ∘ h) (x) = g (h (x))

               = g (x - 7)

              $=(x - 7)^{2}$

Substituting x=5

then,

$(g \circ h) (5)=(5 - 7)^{2}$

Hence option (a) is correct.