How do you evaluate #f(x+1)# given the function #f(x)=3-\frac{1}{2} x#?

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Answer 1 · 2018-05-29T22:00:34

See a solution process below:

To evaluate #f(x + 1)# substitute #color(red)((x + 1))# for each occurrence of #color(red)(x)# in #f(x)# and calculate the result:

#f(color(red)(x)) = 3 - 1/2color(red)(x)# becomes:

#f(color(red)(x + 1)) = 3 - 1/2color(red)((x + 1))#

#f(color(red)(x + 1)) = 3 - 1/2x - (1/2 * 1)#

#f(color(red)(x + 1)) = 3 - 1/2x - 1/2#

#f(color(red)(x + 1)) = 3 - 1/2 - 1/2x#

#f(color(red)(x + 1)) = (2/2 * 3) - 1/2 - 1/2x#

#f(color(red)(x + 1)) = 6/2 - 1/2 - 1/2x#

#f(color(red)(x + 1)) = (6 - 1)/2 - 1/2x#

#f(color(red)(x + 1)) = 5/2 - 1/2x#

Or

#f(color(red)(x + 1)) = (5 - x)/2#