For the function f(x)=(7-8x)^2, find f^-1. Determine whether f^-1 is a function.
For Honors it is
B- Relation t is a function. The inverse of relation t is a function.
A- y=squared x+3 divided by 7
B- The graph with one on the bottom and one on the left side
A- 7 plus minus sign squared x divided by 8. f^-1 is not a function
C- 4
it's clear that the inverse is not a function, since there are a positive and negative value for x that give the same value for y.
y = (7-8x)^2
±y = 7-8x
8x = 7±y
x = (7±y)/8
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To find the inverse function of f(x)=(7-8x)^2, we need to follow these steps:
Step 1: Replace f(x) with y: y = (7-8x)^2.
Step 2: Swap x and y: x = (7-8y)^2.
Step 3: Solve for y: √x = 7-8y.
Rearrange the equation to isolate y:
√x - 7 = -8y.
Divide both sides by -8: y = (7 - √x)/8.
Therefore, the inverse function of f(x) is given by f^(-1)(x) = (7 - √x)/8.
Now, let's determine whether f^(-1) is a function. For f^(-1) to be a function, each value of x must have a unique corresponding value of y.
In this case, for every value of x, there is a unique value of y as long as the expression inside the square root, x, is non-negative. If x is negative, the square root will produce an imaginary number, meaning there will be no real corresponding value of y.
Therefore, f^(-1) is a function as long as x ≥ 0.
B t is inverse not
A
A
A
C 4