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f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
a. The translation f₁(x)=b x-h of f is equivalent to a vertical stretch or compression of f .

Respuesta :

The function f₁(x) can be either vertical stretch or vertical compress: TRUE

What do we mean by Logarithmic Function?

  • The following is the formula for basic logarithmic functions: Where b > 0, f(x) = logbx(r), y = logbx.
  • It is the reciprocal of the exponential function x=b∧y.
  • Log functions are denoted by natural logarithm (ln) and common logarithm (log).

Here are a few examples of logarithmic functions:

  • f(x) = ln (x - 2)
  • g(x) = log2(x + 5)-2
  • h(x) = 2 log x, etc.

So,

Given function:

  • f(x) = bˣ
  • g(x) = logbx

Then,

  • f₁(x)=b^(x-h)
  • f₁(x)=b^x/b^h

Now, Put bˣ=f(x):

  • f₁(x)=f(x)/b^h
  • f₁(x)=b^(-h)f(x)
  • f₁(x)=c f(x)

We discovered that:

  • c=b^(-h)

So, depending on the values of b and h, c can be greater than or less than one.

Therefore, the statement "the function f₁(x) can be either vertical stretch or vertical compress" is TRUE.

Know more about Logarithmic Function here:

https://brainly.com/question/13473114

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