Answer:
(a) f(4) = 11
(b) f(-1) = 211
(c) f(a) = 5a² -55a +151
(d) f(2/m) = (151m² -110m +20)/m²
(e) x = 5 or x = 6
Step-by-step explanation:
A graphing calculator can help with function evaluation. Sometimes numerical evaluation is easier if the function is written in Horner Form:
f(x) = (5x -55)x +151
(a) f(4) = (5·4 -55)4 +151 = -35·4 +151 = -140 +151 = 11
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(b) f(-1) = (5(-1)-55)(-1) +151 = 60 +151 = 211
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(c) Replace x with a:
f(a) = 5a² -55a +151
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(d) Replace x with 2/m; simplify.
f(2/m) = 5(2/m)² -55(2/m) +151 = 20/m² -110m +151
Factoring out 1/m², we have ...
f(2/m) = (151m² -110m +20)/m²
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(e) Solving for x when f(x) = 1, we have ...
5x² -55x +151 = 1
5x² -55x +150 = 0 . . . . subtract 1
x² -11x +30 = 0 . . . . . . . divide by 5
(x -5)(x -6) = 0 . . . . . . . . factor
Values of x that make the factors (and their product) zero are ...
x = 5, x = 6 . . . . values of x such that f(x) = 1
