Given that fx x2 7 match the function g with a transformati

Given that f(x) = x^2 +7, match the function g with a transformation of f g (x) = x^2 11 What is the transformation? g (x) f(x 4) g (x) f(x +4) g (x) f(x +4) g (x) = f(x) - 4 g(x) =f(4x) g(x) = 4f(x)

Solution

First find f(x-4)=(x-4)^2+7=x^2-8x25

f(x)+4=x^2+7+4=x^2+11

f(4x)=(4x)^2+7=16x^2+7

f(x+4)=(x+4)^2+7=x^2+8x+16+7=x^2+8x+23

f(x)-4=x^2+7-4=x^2+3

4f(x)=4(x^2+11)=4x^2+44

so, g(x)=f(x)+4=x^2+11 is correct ......(C)ans