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Functions: If f(x)=3x^2 - 4 and g(x) = x + 3, 1) Evaluate f(3), 2) Find the inverse of f(x) (f^-1(x)), 3)Find fg(x).

in this case x=3 so you substitute it into f(x) to get f(3) = 3(3)² - 4 = 3*9 -4 = 27 - 4 = 232) There are 2 methods to this question, a logical method, and a more mathematical method. Th...

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if y= e^(5x) what is dy/dx

For differentiation it is known that d/dx(e^x) = e^x always.This example is slightly more complex as it includes a product of x as the power.In this case we can simplify the question by setting 5x= u ther...

Answered by Lucinda D. • Maths tutor

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How do you integrate the term x^2?

When integrating terms that include a power, such as x², there is a simple rule to remember. The rule is to add 1 to the power, and then divide the whole term by this number.For example, in the...

Answered by Jack P. • Maths tutor

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Find the partial fraction decomposition of the expression: (4x^2 + x -64)/((x+2)(x-3)(x-4)).

The first step to solving this question is inputting our dummy variables, and laying out the question so we know what we're doing.
So we end up with:(4x² + x - 64)/((x+2)(x-3)(x-4)) =

Answered by Matt V. • Maths tutor

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Given f(x): 2x^4 + ax^3 - 6x^2 + 10x - 84, and knowing 3 is a root of f(x), which is the value of a?

For this exercise we need to be aware of the factor theorem.The factor theorem states when f(c) = 0 then x - c is a factor of the polynomial f(x) and c is a root of f(x). Because we are told that one of t...

Answered by Sabela R. • Maths tutor

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