Consider the function $g(x) = 2 \sin^{-1}(3x)$ - HSC - SSCE Mathematics Extension 1 - Question 5 - 2024 - Paper 1
Question 5
Consider the function $g(x) = 2 \sin^{-1}(3x)$.
Which transformations have been applied to $f(x) = \sin^{-1}(x)$ to obtain $g(x)$?
A. Vertical dilation by a fact... show full transcript
Worked Solution & Example Answer:Consider the function $g(x) = 2 \sin^{-1}(3x)$ - HSC - SSCE Mathematics Extension 1 - Question 5 - 2024 - Paper 1
Step 1
Vertical dilation by a factor of 2
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Answer
The coefficient in front of the sin−1 function, which is 2 in g(x), indicates a vertical dilation by a factor of 2.
Step 2
Horizontal dilation by a factor of \frac{1}{3}
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Answer
The argument of the sin−1 function, 3x, suggests that there is a horizontal dilation. Since we have 3x, this means the dilation factor is 31.
