IB Mathematics Analysis and Approaches Topic SL…

Let $f(x)=e^{kx},\quad g(x)=\ln(x+2),\quad x>-2,\ k>0.$ It is given that $(f\circ g)(3)=4$ .

Determine $k$ correct to 3 significant figures.

Find the composites and their maximal domains.

Solve $(x+2)^k=\ln(2+e^{kx})$ for (3 d.p.) and justify uniqueness.

The function $f$ is defined by $f(x)=\ln(4x)$ , where .

Consider the function $f(x)=7-3e^{-0.4x}$ .

Consider the function $f(x)=4 e^{0.2 x}-2$ .

The function $g$ is defined by $g(x) = \log_3(27x)$ , where . Calculate the exact value of:

Find $(f\circ g)^{-1}(y)$ with domain and range.

Calculate the exact value of $f\left(\frac{e^4}{4}\right)$ .

Calculate the exact value of $f\left(\frac{1}{4}\right)$ .

Determine an expression for the inverse function $f^{-1}(x)$ .

Using your result from part 3, or otherwise, calculate the value of $f^{-1}(-2)$ .

The graph of $y=f\left(\frac{e^3}{4}x^5\right)$ can be generated through a sequence of a vertical stretch and a vertical translation of the graph of . Describe these two transformations, clearly stating the order in which they should be performed.

Write down the domain of $f$ .

Find the y-intercept of the graph of $f$ .

Find $f(4)$ , correct to three significant figures.

Find the smallest integer $x$ such that $f(x)>6.8$ .

Sketch the graph of $f$ . Indicate the y-intercept and the horizontal asymptote.

Write down the domain of $f$ .

Find the y-intercept of the graph of $f$ .

Find $f(3)$ , correct to three significant figures.

Find the smallest integer $x$ such that $f(x)>10$ .

Sketch the graph of $f$ . Indicate the y-intercept and the horizontal asymptote.

$g\left(\frac{1}{27}\right)$ .

Determine an expression for the inverse function $g^{-1}(x)$ .

Using your result from part 3, or otherwise, calculate the value of $g^{-1}(0)$ .

The graph of $y = g(9x^3)$ can be generated through a sequence of a vertical stretch and a vertical translation of the graph of $y = \log_3 x$ . Describe these two transformations, clearly stating the order in which they should be performed.

IB Mathematics Analysis and Approaches SL 2.9—exponential and Logarithmic Functions Questionbank

IB Mathematics Analysis and Approaches SL 2.9—exponential and Logarithmic Functions Questionbank

IB Mathematics Analysis and Approaches SL 2.9—exponential and Logarithmic Functions Questionbank

IB Mathematics Analysis and Approaches SL 2.9—exponential and Logarithmic Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.9—exponential and Logarithmic Functions Questionbank