Operations on Functions

Performing operations on functions involves utilizing mathematical procedures like addition, subtraction, multiplication, division, and composition on single or multiple functions. The outcome of these operations is the creation of new functions, which are instrumental in cracking intricate mathematical challenges and in the modeling of situations in the real world.

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).

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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]

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Arithmetic of Functions

Given two functions,

f (x) = 3 x^{2} + 2 x - 1

and

g (x) = x^{2} - 4

. Find the sum and the product of the two functions.

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Identifying Zeros and Their Multiplicities

Given the function

f (x) = x^{3} - 3 x^{2} - 4 x + 12

, find the zeros of the function and their multiplicities.

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Finding the Inverse

Find the inverse of the function

f (x) = 3 x^{2} + 5

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Function Composition

Let

f (x) = x^{4} & g (x) = 6 x^{4} + 5

. Find

(f \circ g)^{'} (1)

. Type your answer...

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Finding the Slope

Given the functions

f (x) = 3 x^{2} + 2 x - 1

and

g (x) = x - 2

, find the slope of the line tangent to the curve of the function

h (x) = f (g (x))

x = 2

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Operations on Functions

Evaluating Functions

Checking if Continuous Over an Interval

Arithmetic of Functions

Identifying Zeros and Their Multiplicities

Finding the Inverse

Function Composition

Finding the Slope

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