Question

What is the value of (g*h)(-3)?

Answer 1

The correct answer is choice A.

Explanation:

We have given two function.

g(x) = x+1 / x-2

h(x) = 4-x

We have to find the composition of given two functions.

(g*h)(x) = ? and then (g*h)(-3) = ?

(g*h)(x) = g(h(x)

putting the given values of given functions,we have

(g*h)(x) = g(4-x)

(g*h)(x) = 4-x+1 / 4-x-2

(g*h)(x) = 5-x / 2-x

(g*h)(-3) =5-(-3) / 2- (-3)

(g*h)(-3) =5+3 / 2+3

(g*h)(-3) = 8 / 5 Which is the answer.

Answer 2

ANSWER



`\boxed {(g \circ \: h)( - 3) = ( 8)/( 5)}`



EXPLANATION

The given functions are:



`g(x) = (x + 1)/(x - 2)`


and


`h(x) = 4 - x`


Let us find


`(g \circ \: h)(x)`


This implies that,



`(g \circ \: h)(x) = g(h(x))`



`(g \circ \: h)(x) = g(4 - x)`



`(g \circ \: h)(x) = (4 - x + 1)/(4 - x - 2)`



`(g \circ \: h)(x) = (5- x)/(2 - x )`



We now substitute x=-3



`(g \circ \: h)( - 3) = ( 5 - - 3)/( 2 - - 3)`




`(g \circ \: h)( - 3) = ( 8)/( 5)`


The correct answer is A