Given that f : x → 2x-1/x+2, x ≠ -2, find f^{-1}, the inverse of f.

Correct Answer is : f−1:x→1+2x2−x,x≠2f^{-1} : x → 1+2x/2-x, x ≠ 2f−1:x→2−x1+2x,x=2

f^{-1} : x → 1+2x/2-x, x ≠ 2

f^{-1} : x → 1-2x/x+2, x ≠ -2

f^{-1} : x → 1-2x/x-2, x ≠ 2

f^{-1} : x → 1+2x/x+2, x ≠ -2

Correct Answer is : f−1:x→1+2x2−x,x≠2f^{-1} : x → 1+2x/2-x, x ≠ 2f−1:x→2−x1+2x,x=2

Test Index

WAEC Further Mathematics 2015 Paper

Question : 10

Total: 40

Given that

f : x \to \frac{2x-1}{x+2}, x \neq -2

f^{-1}

, the inverse of f.

Solution:

Concept:

The inverse of a function is found by swapping

x

and

y

, then solving for

y

Explanation:

Let

y = f(x) = \frac{2x-1}{x+2}

For the inverse, interchange

x

and

y

x = \frac{2y-1}{y+2}

Multiply both sides by

(y+2)

x(y+2) = 2y-1

Expanding gives:

xy + 2x = 2y - 1

Collect the

y

-terms on one side:

xy - 2y = -1 - 2x

Factor out

y

y(x-2) = -(1+2x)

Divide both sides by

(x-2)

y = -\frac{1+2x}{x-2} = \frac{1+2x}{2-x}

Since

(x-2)

is in the denominator,

x \neq 2

Answer:

f^{-1}: x \to \frac{1+2x}{2-x},\ x \neq 2

Therefore, option A is correct.

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