I have to solve an inverse function.
f(x)=x+6 and g(x)=x+6
f(x)=1/4x,x is equal to or not equal to 0
g(x)=1/4x,x is equal to or not equal to 0
Please help me I have been on this one problem for hours and I can't get it. This one question will determine whether or not I pass this course or not.
what is it you have to solve for?
"an inverse function" doesn't help much
f -1(x)?
g -1(x)?
(f◦g) -1(x)?
In the 2nd part, do you mean
f(x) = 1/(4x) or (1/4)x?
and is g the same as f?
if f and g are inverses, f(g(x)) = x
f(x) = x+6
f(g) = g+6 = (x+6)+6 = x+12
so, f and g are not inverses.
Same for the 2nd part.
If f(x) is the same as g(x), they are not inverses unless
f(x) = x
g(x) = x
i think you have some typos in your write-up.
I did sorry about that but I have found the answer since then. I got it wrong when I submitted it but time was running out. However, I know the answer now but I still don't understand it at all.
To solve for the inverse of a function, you need to follow these steps:
1. Start with the given function, in this case, f(x) = x + 6.
2. Replace f(x) with y, so the function becomes y = x + 6.
3. Swap the x and y variables to obtain the equation x = y + 6.
4. Solve the equation for y.
Subtract 6 from both sides: x - 6 = y.
So, the inverse function is y = x - 6.
Similarly, for g(x) = 1/4x (x is not equal to 0), we can find the inverse function by following the same steps:
1. Start with the given function, g(x) = 1/4x.
2. Replace g(x) with y, so the function becomes y = 1/4x.
3. Swap the x and y variables to obtain the equation x = 1/4y.
4. Solve the equation for y.
Multiply both sides by 4: 4x = y.
So, the inverse function is y = 4x.
Note that the expression "x is equal to or not equal to 0" has no effect on finding the inverse functions, as the process remains the same regardless of the constraints on x.
Now that you have found the inverse functions, you can use them to solve problems or evaluate expressions involving inverse functions.