The functions f:x → 2x2 + 3x -7 and g:x →5x2 + 7x - 6 are defined on the set of real numbers, R. Find the values of x for which 3f(x) = g(x).
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.