Evaluating Functions
Given the operations on functions f(x) = 3x^2 - 4x + 2 and g(x) = 2x - 1, find the value of (f*g)(2).
Checking if Continuous Over an Interval
Determine if the function \(f(x) = \frac{x^2 - 4}{x - 2}\) is continuous over the interval \([-2, 4]\).
Arithmetic of Functions
Given two functions, \(f(x) = 3x^2 + 2x - 1\) and \(g(x) = x^2 - 4\). Find the sum and the product of the two functions.
Identifying Zeros and Their Multiplicities
Given the function \(f(x) = x^3 - 3x^2 - 4x + 12\), find the zeros of the function and their multiplicities.
Finding the Inverse
Find the inverse of the function \(f(x) = 3x^2 + 5\)
Function Composition
Let $f(x)=x^{4} \& g(x)=6 x^{4}+5$. Find $(f \circ g)^{\prime}(1)$.
Type your answer...
Finding the Slope
Given the functions \(f(x) = 3x^2 + 2x - 1\) and \(g(x) = x - 2\), find the slope of the line tangent to the curve of the function \(h(x) = f(g(x))\) at \(x = 2\).