Asked by David Moreno on May 06, 2024

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Evaluate and simplify f(x) =x+2x−3f ( x ) = \frac { x + 2 } { x - 3 }f(x) =x3x+2 at x=x−8x = x - 8x=x8 .

A) f(x−8) =−x−6x−11f ( x - 8 ) = - \frac { x - 6 } { x - 11 }f(x8) =x11x6
B) f(x−8) =x+2x+1f ( x - 8 ) = \frac { x + 2 } { x + 1 }f(x8) =x+1x+2
C) f(x−8) =x−6x+1f ( x - 8 ) = \frac { x - 6 } { x + 1 }f(x8) =x+1x6
D) f(x−8) =x−6x−11f ( x - 8 ) = \frac { x - 6 } { x - 11 }f(x8) =x11x6
E) f(x−8) =x+2x−1f ( x - 8 ) = \frac { x + 2 } { x - 1 }f(x8) =x1x+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.
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Verified Answer

CM
classic margaritaMay 07, 2024
Final Answer :
D
Explanation :
Substituting x−8x-8x8 for xxx in f(x)=x+2x−3f(x) = \frac{x+2}{x-3}f(x)=x3x+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(x8)=(x8)3(x8)+2=x11x6 which matches the expression in choice D. Therefore, the answer is D.