Respuesta :
The correct question is;
The function f(x) = (7^x) + 1 is transformed to function g through a horizontal compression by a factor of 1/3.What is the equation of function g?
Substitute a numerical value for k into the function equation.
g(x) = 7^(kx)
Answer:
Value of k = 1/3 if the function is compressed by compression factor of 1/3.
Step-by-step explanation:
In transformations, the horizontal stretch or compression for a function f(x) is given by g = f(bx) where:
b is a constant.
If b > 0, then the graph of function is compressed.
Now, from the question, we are told that the function is transformed by a compression factor of 1/3.
Function is;f(x) = (7^x) + 1
In transforming to g = f(bx), we have;
g = (7^(x/3)) + 1
Since, we want to find k from the format g = 7^(kx)
Comparing with g = (7^(x/3)) + 1, we cans see that ; k = 1/3
The function g(x) is, [tex]g(x)=7(\frac{1}{3}x )+1[/tex]
The value of k is [tex]\frac{1}{3}[/tex]
To understand more, check below explanation.
Compression of function:
The given function is,
[tex]f(x)=7x+1[/tex]
We have to find function g(x) from f(x) after compression by a factor of 1/3.
To find g(x), replace x by [tex]\frac{1}{3}x[/tex].
[tex]g(x)=7(\frac{1}{3}x )+1\\\\g(x)=\frac{7}{3}x+1[/tex]
Thus, the value of k is [tex]\frac{1}{3}[/tex]
Learn more about the linear function here:
https://brainly.com/question/15602982
