The functions \(f:x \to 2x^2 + 3x -7\) and \(g:x \to 5x^2 + 7x - 6\) are defined on the set of real numbers, R. Find the values of \(x\) for which \(3f(x) =...

Assessment: WAEC SSCE - Further Mathematics - 2022 (Objective) Subject: Further Mathematics

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The functions \(f:x \to 2x^2 + 3x -7\) and \(g:x \to 5x^2 + 7x - 6\) are defined on the set of real numbers, R. Find the values of \(x\) for which \(3f(x) = g(x)\).

x = -3 or -5

x = -3 or 5

x = 3 or -5

x = 3 or 5

Answer Details

To find the values of x for which 3f(x) = g(x), we need to substitute the given functions f(x) and g(x) and then solve for x. Substituting the function f(x) = 2x^2 + 3x - 7, we get: 3f(x) = 3(2x^2 + 3x - 7) = 6x^2 + 9x - 21 Substituting the function g(x) = 5x^2 + 7x - 6, we get: g(x) = 5x^2 + 7x - 6 Now we can set these two equations equal to each other and solve for x: 6x^2 + 9x - 21 = 5x^2 + 7x - 6 Subtracting 5x^2 and 7x from both sides, we get: x^2 + 2x - 15 = 0 Factoring this quadratic equation, we get: (x + 5)(x - 3) = 0 Therefore, the values of x that satisfy the equation 3f(x) = g(x) are x = -5 and x = 3. Hence, the answer is: x = -5 or 3.

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The functions \(f:x \to 2x^2 + 3x -7\) and \(g:x \to 5x^2 + 7x - 6\) are defined on the set of real numbers, R. Find the values of \(x\) for which \(3f(x) =...

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