Q. For a given input value x, the function g outputs a value y to satisfy the following equation.−4x−6=−5y+2Write a formula for g(x) in terms of x.g(x)=□
Isolate y in the equation: First, we need to isolate y on one side of the equation to solve for g(x) in terms of x. The given equation is −4x−6=−5y+2.
Move terms involving to one side: Add to both sides of the equation to move the terms involving y to one side: −4-4−4x - 666 + 555y = 222.
Move constant term to the other side: Now, subtract 222 from both sides to move the constant term to the other side: −4x−6+5y−2=0-4x - 6 + 5y - 2 = 0−4x−6+5y−2=0.
Combine like terms: Combine like terms on the left side of the equation: −4x−8+5y=0-4x - 8 + 5y = 0−4x−8+5y=0.
Isolate the term with yyy: Add 4x+84x + 84x+8 to both sides to isolate the term with yyy: 5y=4x+85y = 4x + 85y=4x+8.
Solve for y: Finally, divide both sides by 555 to solve for yyy: y=4x+85y = \frac{4x + 8}{5}y=54x+8.
Write the function g(x) g(x) g(x): Since g(x) g(x) g(x) outputs y y y, we can write the function as g(x)=4x+85 g(x) = \frac{4x + 8}{5} g(x)=54x+8.
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