Answer:
x = -1.5, +2.0
Explanation:
You want to solve the equation f(x²) = x-1, given that f(x) = 2x -7.
Solution
First, we find the meaning of f(x²) by putting x² into the function definition where x is:
f(x²) = 2(x²) -7
Then, we set that equal to x-1 and solve the resulting quadratic.
2x² -7 = x -1
2x² -x -6 = 0 . . . . . . . subtract (x-1)
(2x +3)(x -2) = 0 . . . . factor
The solutions to this are the x-values that make the factors zero:
2x +3 = 0 ⇒ x = -3/2
x -2 = 0 ⇒ x = 2
The solutions are x = -3/2 and x = 2.
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Additional comment
The attached graph solves the equation we get when we subtract (x-1) from both sides of what you're trying to solve. The solutions are the x-intercepts of the graph.
The factoring can be done by splitting the x-term into two parts. Their product is the product of the first and last terms.
2x² -x -6 = 0
2x² -4x +3x -6 = 0 . . . . . 2·(-6) = -12 = (-4)(3) and -4+3=-1, the x-coefficient
2x(x -2) +3(x -2) = 0 . . . . factor each pair of terms
(2x +3)(x -2) = 0 . . . . . . . factor out the common factor