Question

Suppose g(x)=f(2x) when f(x)=x^2-4x-5. Find the standard expression for g(x).

Please show steps.

Answer 1

we have that

f(x)=x²-4x-5 g(x)=f(2x)

step 1
find --------> f(2x)
that means that the variable is now going to be 2x instead of x
so
f(2x)=(2x)²-4(2x)-5------------> 4x²-8x-5

therefore

f(2x)=4x²-8x-5
and
g(x)=4x²-8x-5

the answer is
g(x)=4x²-8x-5