Linear Functions (Grade 12 NSC Matric Mathematics): Quizzes

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Linear Functions
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What does an inverse function do to the original function?

It reverses the effect

What does the notation f−1(x)f^{-1}(x) represent?

The inverse function of f(x)f(x)

What is the first step in finding the inverse of a linear function?

Interchange xx and yy

For which value of aa does a linear function y=ax+qy = ax + q NOT have an inverse?

a=0a = 0

How are the graphs of f(x)f(x) and f−1(x)f^{-1}(x) related?

Reflections about y=xy = x

How do domain and range change from ff to f−1f^{-1}?

They swap positions

What is the inverse of f(x)=2x−3f(x) = 2x - 3?

f−1(x)=x2+32f^{-1}(x) = \frac{x}{2} + \frac{3}{2}

If f(x)f(x) has y-intercept (0,q)(0, q), what is the x-intercept of f−1(x)f^{-1}(x)?

(q,0)(q, 0)

How can you verify that you've found the correct inverse function?

Check that f(f−1(x))=xf(f^{-1}(x)) = x

What is the general inverse of y=ax+qy = ax + q (where a≠0a \neq 0)?

y=1ax−qay = \frac{1}{a}x - \frac{q}{a}

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