Problem:
f(x) = x^3 + x + 1
Question:
What is f^-1(x)? What is f^-1(0.5)?
How would we change this equation into it's inverse? Do we solve for x such as this?
y = x^3 + x + 1
y - 1 = x(x^2 + 1)
I don't see "What is f^-1(x)?" asked in this attachment. Next time give the actual question, not your (incorrect) interpretation of the question.
Let $\displaystyle f^{-1}(1/2) = a$.
Since (1/2, a) is a point on the graph of $\displaystyle y = f^{-1}(x)$ it follows that (a, 1/2) is a point on y = f(x).
Therefore $\displaystyle \frac{1}{2} = a^3 + a + 1 \Rightarrow a^3 + a + \frac{1}{2} = 0$ and you're expected to use technology to solve this equation.