Composite and inverse functions

g (x) = 4x²

Find f (9)

Solve fg (x) 0 Show clear algebraic working.

The function f is defined as

State the value of x that cannot be included in any domain of the function f

Express the inverse function f^–1 in the form f^–1(x) =...

f^–1(x) =_........

The functions f and g are such that

State which value of x cannot be included in any domain of g

Find fg(4)

The function h is such that

Express the inverse function h⁻¹ in the form h¹:x ...

The functions g and h are such that

h(x) = x² + 4 x 0

What value of x must be excluded from any domain of g?

Solve gh(x) = 1

The function f is such that

Find f^–1(x)

The function g is such that

Express g(x) in the form a(x – b)² + c

18The function f is such that f(x) = where x ≠ 0 and k is an integer.

Express the inverse function f⁻¹ in the form f⁻¹(x) =...

The function g is such that g(x) = 2 – 3x⁴ where x ≠ 0 The function h is such that h(x) = where x ≠ 2

Find g(−2)

Express the composite function hg in the form hg(x) =... Give your answer in its simplest form.

hg(x) =_........

25The function f is such that f(x) = 3x² – 12x + 7 where x ≤ 2 Express the inverse function f^–1 in the form f^–1(x) = …

f^–1(x) =_........

The function f is defined as

Find f(10)

Express the inverse function f⁻¹ in the form f⁻¹:x …

f⁻¹:x _........

19f(x) = x² – 4

g(x) = 2x + 1

Solve fg(x) 0 Show clear algebraic working.

The functions f and g are such that

The function h is such that h(x) = fg(x)

The domain of h is {x: x ≤ 6} Express the inverse function h^–1 in the form h^–1(x) =...

h^–1(x) =_........

The function g is defined as

Express the inverse function g⁻¹ in the form g⁻¹:x …

g⁻¹:x _........

State the domain of g⁻¹

The functions f and g are defined as

f(x) = x² + 6 g(x) = x – 10

Find fg(3)

Solve the equation fg(x) = f(x) Show clear algebraic working.

The function h is defined as

State the value of x that cannot be included in the domain of h

Express the inverse function h^–1 in the form h^–1(x) =...

h^–1(x) =_........

The functions f and g are defined as

f:x 5x – 7

Write down the value of x that must be excluded from any domain of g

Find gf(2.6)

Solve fg(x) = 2

Express the inverse function g^–1 in the form g^–1:x ...

g^–1:x _........

21The function f is such that f(x) = 5 + 6x – x²for x ≤ 3

Express 5 + 6x – x² in the form p – (x – q)² where p and q are constants.

Using your answer to part (a), find the range of values of x for which f^–1(x) is positive.

Find f (1)

State the range of the function f.

The function g is such that g(x) = x ≠−3

Work out fg(2)

The functions f and g are such that

The function h is such that h(x) = fg(x) for x −2 Express the inverse function h⁻¹(x) in the form h⁻¹(x) = …

The functions f and g are defined as

State which value of x must be excluded from any domain of the function f.

Find fg(x). Simplify your answer.

fg(x) =_........

Express the inverse function f in the form f (x) = …

f (x) =_........

Part of the curve with equation y = h(x) is shown on the grid.

Find an estimate for the gradient of the curve at the point where x Show your working clearly.

The function f is such that f (x) = 3 x – 2

Find f (5)

The function g is such that g(x) = 2x² – 20x + 9 where x 5

Express the inverse function g^–1 in the form g^–1(x) =...

g^–1(x) =_........

The function f is such that

Find f (–7)

Express the inverse function f^–1 in the form f^–1(x) =...

The function g is such that

Find fg (3)

Which values of x cannot be included in any domain of g?

Two functions, f and g are defined as

Given that h = fg

express the inverse function h in the form h: x …

h: x _........