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hich represents the inverse of the function f(x) = 4x?
Oh(x)=x+4
Oh(x)=x-4
h(x) = ²x
h(x) = x

Sagot :

Leora03

Answer:

[tex]h(x) = \frac{1}{4} x[/tex]

Step-by-step explanation:

To find the inverse of a function, the steps are:

  1. Let y= f(x)
  2. Make x the subject of formula
  3. Replace x with f⁻¹(x) and y with x

In this case, since h(x) is the inverse function of f(x), we can replace x with h(x) in step 3.

_____

f(x)= 4x

Let y= f(x) [tex]\textcolor{steelblue}{\text{ - step 1}}[/tex]

y= 4x

Divide both sides by 4:

[tex] \frac{1}{4} y = x[/tex]

[tex]x = \frac{1}{4} y \: \: \: \textcolor{steelblue}{\: \text{ - step 2}}[/tex]

Replace x with h(x) and y with x:

[tex]\bf{h(x) = \frac{1}{4} x} \: \: \: \textcolor{steelblue}{\: \text{ - step 3}}[/tex]

Additional:

For a similar question on inverse functions, do check out the following!

  • https://brainly.com/question/21287415
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