Problem

Let the relation \( R \) be defined on the set of real numbers by \( R = \{(x, y) | x = 2y + 3\} \). Find the inverse of the relation \( R \).

Answer

Expert–verified
Hide Steps
Answer

Finally, write the equation for the inverse relation in the form \( y = g(x) \), which gives \( y = 2x + 3 \).

Steps

Step 1 ：Write the equation for the relation in the form \( y = f(x) \), which gives \( y = \frac{x - 3}{2} \).

Step 2 ：The inverse of a relation is found by exchanging \( x \) and \( y \). So, replacing \( x \) with \( y \) and \( y \) with \( x \), we get \( x = \frac{y - 3}{2} \).

Step 3 ：Finally, write the equation for the inverse relation in the form \( y = g(x) \), which gives \( y = 2x + 3 \).

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More