Question

how do I find the inverse of the function f(x)= 4x^3 -3 algebraically?

Answer 1

1. Replace f(x) with y.
2. Switch x and y.
3. Solve for y.
4. Replace y with \(f^{-1}(x) \).

Answer 2

try to solve for x
Once you have x , you'll switch x and y; the y is the inverse.

Answer 3

what about the x^3?

Answer 4

Same steps explained above.

for \(x^3\), you have \[y=x^3\\ x = y^3\\ \sqrt[3]{x}=y \\ \boxed{\sqrt[3]{x}=f^{-1}(x)}\]

Answer 5

y=4x^3-3
x=4y^3-3
x+3=4y^3
x+3/4=y^3
the cube root\[\sqrt[3]{?x+3/4}=y\]

Answer 6

the whole cube root is over 4 tho not just the 3 which is how it looks cuz I tried to use the equations thingie

Answer 7

\( f(x)= 4x^3 -3\)
1. \( y = 4x^3 -3\)
2. \( x = 4y^3 -3\)
3.
\( x = 4y^3 -3\)

\(x + 3= 4y^3 \)

\(4y^3 = x + 3 \)

\(y^3 = \dfrac{x + 3}{4} \)

\(y = \sqrt[3]{ \dfrac{x + 3}{4} } \)

4. \(f^{-1}(x) = \sqrt[3]{ \dfrac{x + 3}{4} } \)