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A function $f(x)$ is defined by $f(x) = \frac{2}{x} + 3$, $x > 0$ - Scottish Highers Maths - Question 6 - 2023

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Question 6

A-function-$f(x)$-is-defined-by-$f(x)-=-\frac{2}{x}-+-3$,-$x->-0$-Scottish Highers Maths-Question 6-2023.png

A function $f(x)$ is defined by $f(x) = \frac{2}{x} + 3$, $x > 0$. Find the inverse function, $f^{-1}(x)$.

Worked Solution & Example Answer:A function $f(x)$ is defined by $f(x) = \frac{2}{x} + 3$, $x > 0$ - Scottish Highers Maths - Question 6 - 2023

Step 1

Step 1: Express in terms of $y$

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Answer

Let y=f(x)=2x+3y = f(x) = \frac{2}{x} + 3. To find the inverse, we first need to express xx in terms of yy.

Step 2

Step 2: Rearranging the equation

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Answer

Subtract 3 from both sides: y−3=2xy - 3 = \frac{2}{x} Now, multiply both sides by xx: (y−3)x=2(y - 3)x = 2 Next, solve for xx: x=2y−3x = \frac{2}{y - 3}

Step 3

Step 3: State the inverse function

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Answer

The inverse function is: f−1(x)=2x−3f^{-1}(x) = \frac{2}{x - 3}

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