Find the formula for the inverse of each funtion.
3.) f(x)= 2x-5 for this one I have
y= (x+5)/2 is this correct?
4.) g(x)= (x+5)^3
I am stuck on this one.
3 is good
4:
let y = (x+5)^2
interchange x with y
x = (y+5)^2
+-sqrt(x) = y+5
y = -5 +-sqrt(x) or f(x) = -5 +-sqrt(x)
Hi Reiny,
I just have one question for 4.) the problem is g(x)= (x+5)^3
how were you able to convert the equation to the following?
let y = (x+5)^2
interchange x with y
x = (y+5)^2
my error, did not read the question carefully enough, thought it was squared instead of cubed.
so just change the sqrt to cube root and use only the positive sign.
so last line should be
y = -5 +-cuberoot(x)
To find the inverse of a function, you need to switch the roles of x and y and solve for y.
For function f(x) = 2x - 5:
Step 1: Replace f(x) with y: y = 2x - 5.
Step 2: Swap x and y: x = 2y - 5.
Step 3: Solve for y: Add 5 to both sides of the equation to isolate 2y: x + 5 = 2y.
Step 4: Divide both sides of the equation by 2 to solve for y: (x + 5) / 2 = y.
Therefore, the inverse of function f(x) = 2x - 5 is y = (x + 5) / 2.
Now let's move on to function g(x) = (x + 5)^3:
Step 1: Replace g(x) with y: y = (x + 5)^3.
Step 2: Swap x and y: x = (y + 5)^3.
At this point, finding a formula for the inverse of this function becomes more challenging. Instead of trying to solve the equation directly, we can use a different approach.
Step 3: Take the cube root of both sides to eliminate the power of 3: ∛(x) = ∛((y + 5)^3).
Step 4: Simplify the right side: ∛(x) = y + 5.
Step 5: Subtract 5 from both sides of the equation to solve for y: ∛(x) - 5 = y.
Therefore, the inverse of function g(x) = (x + 5)^3 is y = ∛(x) - 5.
Please note that when finding the inverse of a function, it is crucial to verify if the inverse is indeed a valid function by checking if it passes the horizontal line test.