# Given f(x) = x² and g(x) = 5x + 3 Evaluate i) gf(-2) ii) g¯¹(x)

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i) gf(-2)

Given two function g(x) and f(x), the function gf(x) = g[f(x)]

it is given:

g(x) = 5x + 3, and f(x) = x^2

Therefore:

gf(x) = g[f(x)] = g(x^2) = 5(x^2) + 3

= 5x^2 + 3

And

gf(-2) = 5(-2)^2 + 3 = 5*4 +3 = 20 + 3 = 23

ii) g¯¹(x)

When gx has the form y = g(x),

g inverse(x) represents the same function in the form;

x = a function of y

We convert g(x) in the g (inverse(x) form as follows:

y = 5x +3

5x = y - 3

x = y/5 - 3/5

Interchanging x and y, the function g inverse(x) becomes

g inverse(x) --> y = x/5 - 3/5

**Given f(x) = x² and g(x) = 5x + 3**

Evaluate

i) gf(-2)

ii) g¯¹(x)

Solution:

i)

gf(-2) =g {(-2)^2} = g(4) =5*4+3=23

ii)

g inverse (x).

g(x) = 5x+1. Or

y = 5x+1. Or

x = (y-1)/5. Or Changing x and y,

g inverse x = y = (x-1)/5 .