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3 years ago

What is the inverse of the function f(x)

Mathematics

1 answer:

Anon25 [30]3 years ago

5 0

Answer:

$h(x)= 9x - 18$

Step-by-step explanation:

Given

$f(x) = \frac{1}{9}x + 2$

Required

The inverse

$f(x) = \frac{1}{9}x + 2$

Replace f(x) with y

$y = \frac{1}{9}x + 2$

Swap x and y

$x = \frac{1}{9}y + 2$

Subtract 2

$x - 2= \frac{1}{9}y$

Multiply 9

$9x - 18 = y$

Rewrite as:

$y = 9x - 18$

So:

$h(x)= 9x - 18$

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The function f(x) = One-sixth (two-fifths) Superscript x is reflected across the y-axis to create the function g(x). Which order

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The ordered pair (-3 , $\frac{4}{375}$ ) is on g(x) ⇒ 1st answer

Step-by-step explanation:

Let us revise the reflection across the axes

If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x) (change the sign of y)
If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x) (change the sign of x)

∵ $f(x)=\frac{1}{6}(\frac{2}{5})^{x}$

∵ f(x) is reflected across the y-axis to create the function g(x)

- Change the sign of x

∴ $g(x)=\frac{1}{6}(\frac{2}{5})^{-x}$

To find the point that lies on g(x) substitute x in g(x) by the x-coordinate of the point if the answer equal to the y-coordinate of the point, then the point lies on it if not then the point does not lie on it

∵ The coordinates of the point are (-3 , $\frac{4}{375}$ )

∴ x = -3 and y = $\frac{4}{375}$

- Substitute x by -3 in g(x)

∵ $g(x)=\frac{1}{6}(\frac{2}{5})^{-x}$

∴ $g(x)=\frac{1}{6}(\frac{2}{5})^{-(-3)}$