Asked by David Moreno on May 06, 2024
Verified
Evaluate and simplify f(x) =x+2x−3f ( x ) = \frac { x + 2 } { x - 3 }f(x) =x−3x+2 at x=x−8x = x - 8x=x−8 .
A) f(x−8) =−x−6x−11f ( x - 8 ) = - \frac { x - 6 } { x - 11 }f(x−8) =−x−11x−6
B) f(x−8) =x+2x+1f ( x - 8 ) = \frac { x + 2 } { x + 1 }f(x−8) =x+1x+2
C) f(x−8) =x−6x+1f ( x - 8 ) = \frac { x - 6 } { x + 1 }f(x−8) =x+1x−6
D) f(x−8) =x−6x−11f ( x - 8 ) = \frac { x - 6 } { x - 11 }f(x−8) =x−11x−6
E) f(x−8) =x+2x−1f ( x - 8 ) = \frac { x + 2 } { x - 1 }f(x−8) =x−1x+2
Simplify
To reduce a mathematical expression or equation to its simplest form by performing operations and combining like terms.
Evaluate
To calculate the numerical value of an expression or determine the result of an equation.
- Examine and simplify fractions that contain polynomials in both the numerator and denominator.
- Evaluate functions by inserting predetermined values into expressions.
Verified Answer
CM
classic margaritaMay 07, 2024
Final Answer :
D
Explanation :
Substituting x−8x-8x−8 for xxx in f(x)=x+2x−3f(x) = \frac{x+2}{x-3}f(x)=x−3x+2 gives f(x−8)=(x−8)+2(x−8)−3=x−6x−11f(x-8) = \frac{(x-8)+2}{(x-8)-3} = \frac{x-6}{x-11}f(x−8)=(x−8)−3(x−8)+2=x−11x−6 which matches the expression in choice D. Therefore, the answer is D.
Learning Objectives
- Examine and simplify fractions that contain polynomials in both the numerator and denominator.
- Evaluate functions by inserting predetermined values into expressions.