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Find the inverse of the function with a and b representing positive real numbers.\ f(x) = ax^3 + b\ f^{-1}(x) = \\ on domain (-?,?) 

          Find the inverse of the function with a and b representing positive real numbers.\
f(x) = ax^3 + b\
f^{-1}(x) = \\
on domain (-?,?)
Find the inverse of the function with a and b representing positive real numbers.f(x) = ax^3 + bf^-1(x) = on domain (-?,?)

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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Find the inverse of the function with a and b representing positive real numbers. f(x)=ax^(3)+b f^(-1)(x)= Find the inverse of the function with a and b representing positive real numbers f(x)=ax3+b f-1(x)= on domain(-)
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Transcript

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00:01 Let's determine the inverse of this function.
00:04 So here we have the function, if of x equals a square root of a x plus b, x is greater than or equal 0 and a and b are two positive real numbers.
00:15 And so to determine the inverse of the function, we follow a few steps.
00:19 In step one, we replace f of x by y.
00:26 So i'm going to replace f of x by y.
00:29 And so the equation now becomes y equals square root of, a x plus b in step two we interchange x and y that is x will be replaced as y and y and y will be replaced as x so from the equation y equals square root of a x plus b replace all y by x and replace all x by y and so therefore this equation now becomes x equals square root of a x plus b.
01:09 In step three, we solve for y, solve y.
01:19 So let's consider this equation.
01:21 X equals square root of a y plus p.
01:27 To solve for y, let's square both side.
01:29 So we squared this side.
01:31 We also square this side.
01:33 Square of x is x squared.
01:36 Then we have a square root and we squared up...
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