Determining composite and inverse functions test questions

1

What does \({x^2} + 4x - 5\) expressed in the form \({(x + a)^2} + b\) equal?

2

What could the graph below represent?

A sine graph that touches points (0,1) and (135,0)

3

If \(h(x) = {x^3}\) and \(f(x) = \cos 2x\), what is \(f(h(x))\) equal to?

4

If \(f(x) = 3{x^2}\) and \(g(x) = x - 4\), what is \(g(f(x))\) equal to?

5

Functions 'g' and 'h' are defined by \(g(x) = \frac{1}{x}\) and h(x) = 8 - 5x where \(x \in R\). What does \(h(g(x))\) equal?

6

When \(2{x^2} + 8x - 3\) is written in the form \(a{(x + b)^2} + c\), what are the values of 'a', 'b' and 'c'?

7

What is \(9 - 4x - {x^2}\) expressed in the form \(9 - {(x + q)^2}\) equal to?