Find the domain and range of the inverse
f(x)=-4x-2
y=-4x-2
x=-4y-2
x+2/-4=-4y/-4
f(x)=x+2/-4
answer:
domain (all real numbers)
range (all real numbers)
To find the domain and range of the inverse of a function, you need to first find the inverse function itself. Let's start by finding the inverse of f(x)=-4x-2.
Step 1: Replace f(x) with y:
y = -4x - 2.
Step 2: Swap x and y:
x = -4y - 2.
Step 3: Solve for y:
x + 2 = -4y.
(-1/4)(x + 2) = y.
y = (-1/4)x - 1/2.
Now, we have the inverse function:
f^(-1)(x) = (-1/4)x - 1/2.
Domain:
The domain of f^(-1)(x) will be the same as the range of the original function f(x).
For f(x)=-4x-2, the domain is all real numbers.
Therefore, the domain of the inverse function f^(-1)(x) is also all real numbers.
Range:
Similarly, the range of f^(-1)(x) will be the same as the domain of the original function f(x).
For f(x)=-4x-2, we can see that the equation is in the form y = mx + b, where m is the slope (-4 in this case).
Since the slope is negative, the range of the original function is also all real numbers.
Therefore, the range of the inverse function f^(-1)(x) is also all real numbers.
So, the domain and range of the inverse function f^(-1)(x) are both all real numbers.