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f(x) = 5 – x and g(x) = 3x + 7 (a) Simplify f(2x) + g(x – 1)

May look hard at first but once understood is simple.Question is asking to add two functions together.Firstly we begin by calculation f(2x) We know that f(x) = 5 – x, to find f(2x) we replace the x by 2xT...

Answered by Matthew B. • Maths tutor

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Write x^2+4x-12 in the form (x+a)^2+b where a and b are constants to be determined.

This method is known as completing the square. To find the constant a, we must halve the coefficient of x, which in this case is 4. This is to compensate for the double term when expanding the brackets. S...

Answered by Priya G. • Maths tutor

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A curve (a) has equation, y = x^2 + 3x + 1. A line (b) has equation, y = 2x + 3. Show that the line and the curve intersect at 2 distinct points and find the points of intersection. Do not use a graphical method.

a) y = x² + 3x + 1b) y = 2x + 3At points of intersection (a) = (b).2x + 3 = x ² + 3x + 1Note this is a quadratic expression which will solve for 2 unique solutions, providing the dis...

Answered by Joseph C. • Maths tutor

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Find the inverse of: f(x) = (2x + 3)/(x - 4)

To find the inverse of a function, f^-1(x):1) set f(x) as y: y = (2x + 3)/(x - 4)2) swap x and y: x = (2y + 3)/(y -4)3) solve the new equation for y: x(y -4) = 2y + 3 = xy -4x2y - xy = -4x - 3y...

Answered by Sophie I. • Maths tutor

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Can you explain when we flip the inequality direction when solving inequalities.

We solve inequalities exactly like normal equations except for Dividing by a Negative Coefficient where we Change the inequality directionE.gx+2>4 is ... x>2 (ask second ...

Answered by Matthew M. • Maths tutor

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