For each pair of functions, find f(g(x)) and g(f(x)). Simplify your answers.

Question

1. f(x)= 1/x-6, g(x)= 7/x+6
2. f(x)= x^2 +1, g(x)= SqRt x+2
3. f(x)= |x|, g(x)= 5x+1

Answer 1

To answer a problem like this, we substitute one function in place of the x in the other function.

For example, in problem 2 we have f(x) = x² and g(x) = √x +2 (I'm assuming that it's √x and not √(x+2)

To find f(g(x)), we take f(x) and everywhere there's an x, we replace it with g(x).

f(x) = x²

f(g(x)) = g(x)²

= (√x + 2)²

= x + 2√x + 4

To find g(f(x)), we take g(x) and everywhere there's an x, we replace it with f(x)

g(x) = √x + 2

= √(x²) + 2

= x+ 2

The other 2 problems would be solved the same way