# 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?

### 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?