Respuesta :
The inverse of f₁(x)=b^(x-h) is not equal to a vertical stretch or compression of g: TRUE
What accurately do we mean by Logarithmic Functions?
- The logarithmic function is the inverse of the exponential function.
- A logarithm to the base b is the power to which b must be increased in order to obtain a specific number.
- For example, log28 is the power to which 2 must be raised to generate eight.
- Clearly, 23 = 8, so log28=3.
So,
Given inverse function: f₁(x)=b^(x-h)
First, find out the inverse of this function.
- So, let f₁(x) = y
- Then, y=b^(x-h)
Switch the variables x & y as follows;
- x=b^(y-h)
Solve for y as shown below and take logarithm both sides:
- log(x) = (y-h)log(b)
- y=h+ log(x)/log(b)
So,
- f₁^(-1)(x)= h+log(x)/log(b)
- f₁^(-1)(x)= h+logb(x)
- f₁^(-1) (x)= g(x)+h
From the first equation we get the inverse of as f₁ follows:
- f₁^(-1) (x)= g(x)+h
Therefore, the statement "the inverse of f₁(x)=b^(x-h) is not equal to a vertical stretch or compression of g" is TRUE.
Know more about Logarithmic Functions here:
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