Question

Define *G*: ℝ → ℝ by the rule G(x) = 2 − 3x for each real
number *x*. Prove that *G* is onto.

**Proof that G is onto:** Let

Enter the result - an expression in *y* - in the box
below.)

x=________

To finish the proof, we need to show (1) that *x* is a
real number, and (2) that G(x) = y.

Now sums, products, and differences of real numbers are real
numbers, and quotients of real numbers with nonzero denominators
are also real numbers. Therefore, *x* is a real number.

In addition, according to the formula that defines *G*,
when *G* is applied to *x*, *x* is multiplied
by 3 and the result is subtracted from 2.

When the expression for *x* (using the variable
*y*) is multiplied by 3, the result is ______. And when the
result is subtracted from 2, we obtain ______. Thus G(x) = y.
Hence, there exists a number *x* such that *x* is a
real number and G(x) = y. Therefore, *G* is onto.

Answer #1

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