Inverse Functions (Grade 12 NSC Matric Mathematics): Quizzes

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

Reverses or undoes the operation

What property must a function have to be invertible?

It must be a one-to-one relation

What is the first step when finding the inverse of a function?

Interchange xx and yy

If f(x)=3x−5f(x) = 3x - 5, what is f−1(x)f^{-1}(x)?

x+53\frac{x + 5}{3}

How are a function and its inverse related graphically?

Reflections about the line y=xy = x

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

The inverse function

If g(x)=5xg(x) = 5x, what is g−1(x)g^{-1}(x)?

x5\frac{x}{5}

How can you verify that f−1f^{-1} is the correct inverse of ff?

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

Why is f(x)=3x2f(x) = 3x^2 not invertible?

Inverse gives two outputs per input

What is true about points on the line y=xy = x?

xx- and yy-coordinates are equal

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