Let p(x)=2x^3-113 and let q be the inverse of p. Find q(137). Please explain in steps.
I posted this already but I did not list my steps. The first step would be to find the inverse of 2x^3-113 which would be: y=(x+113/2)^1/3. and then would I just plut in 137 for x?
q = [ (x+113)/2 ]^1/3
q = [ (137+113)/2 ]^1/3
q = 125^1/3 = 5
To find the value of q(137), we need to find the inverse function of p(x) = 2x^3 - 113 and evaluate it at x = 137.
Step 1: Start with the function p(x) = 2x^3 - 113.
Step 2: Replace p(x) with y to get the equation y = 2x^3 - 113.
Step 3: Swap x and y to get the equation x = 2y^3 - 113.
Step 4: Solve the equation x = 2y^3 - 113 for y. We want to isolate y, so let's get rid of the -113 first. Add 113 to both sides: x + 113 = 2y^3.
Step 5: Divide both sides by 2: (x + 113)/2 = y^3.
Step 6: Take the cube root of both sides to solve for y: y = (x + 113)/2^(1/3).
Step 7: Now, we can substitute x = 137 into the equation we found in step 6: y = (137 + 113)/2^(1/3).
Step 8: Simplify the expression: y = 250/2^(1/3).
Thus, q(137) = 250/2^(1/3).