Question

Let f(x) = x + 2 and g(x) = x2 Find ( g o f)(-­5)

Answer 1

f(x) = x + 2
g(x) = x²

(g ο f)(-5) = g(f(-5))
(g ο f)(-5) = (-5 + 2)²
(g о f)(-5) = (-3)²
(g о f)(-5) = 9

Answer 2

(g o f)(-5)= 9

Explanation:

Given :
`f(x) = x+2`

`g(x)=x^(2)`

To Find : (g o f )(-5)

Solution :

We are supposed to find the value of (g o f )(-5)

So, first understand that (g o f )(x) means g(f(x))

Now putting value of x :

(g o f )(x) =g(f(x))

⇒(g o f)(-5)= g(f(-5)) --(a)

Now for solving further we need to find value of f(-5)

Since we are given that
`f(x) = x+2`

⇒
`f(-5) = -5+2`

⇒
`f(-5) = -3`

Now put this value in (a)

⇒(g o f)(-5)= g(-3) ----(b)

Now we need to calculate the value of g(-3)

Since we are given that

`g(x)=x^(2)`

⇒
`g(-3)=(-3)^(2)`

⇒
`g(-3)=9`

now put this value in (b)

⇒(g o f)(-5)= 9

Hence , (g o f)(-5)= 9