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Given the functions f(x) = x - x and g(x)= x² â€" 3x -12,a)solve the equation f(x) = 6b )solve the equation f(x) = g(x).

User Ahtartam
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a) To solve the equation f(x) = 6, we need to substitute the expression for f(x) into the equation and solve for x.

Given that f(x) = x - x, we can rewrite the equation as x - x = 6.

Simplifying, we have 0 = 6.

Since there is no value of x that satisfies this equation, there is no solution for f(x) = 6.

b) To solve the equation f(x) = g(x), we need to substitute the expressions for f(x) and g(x) into the equation and solve for x.

Given that f(x) = x - x and g(x) = x² - 3x - 12, we can rewrite the equation as x - x = x² - 3x - 12.

Simplifying, we have 0 = x² - 3x - 12.

To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring, we get (x - 4)(x + 3) = 0.

Setting each factor equal to zero, we have x - 4 = 0 and x + 3 = 0.

Solving these equations, we find x = 4 and x = -3.

Therefore, the solutions to the equation f(x) = g(x) are x = 4 and x = -3.

User Mansur Ashraf
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