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# help asap pls

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1.) Let $f(x)=\left\lfloor\left(-\frac58\right)^x\right\rfloor$ be a function that is defined for all values of $x$ in $[0,\infty)$ such that $f(x)$ is a real number. How many distinct values exist in the range of $f(x)$?

2.) Let $f(x) = \left\{\begin{array}{cl}ax+3 & \text{ if }x>0, \\ab & \text{ if }x=0, \\bx+c & \text{ if }x<0.\end{array}\right.$If $f(2)=5$, $f(0)=5$, and $f(-2)=-10$, and $a$, $b$, and $c$ are nonnegative integers, then what is $a+b+c$?

WITH LATEX:

1.) Let $$f(x)=\left\lfloor\left(-\frac58\right)^x\right\rfloor$$ be a function that is defined for all values of $$x$$ in $$[0,\infty)$$ such that $$f(x)$$ is a real number. How many distinct values exist in the range of $$f(x)$$?

2.) Let

$$f(x) = \left\{\begin{array}{cl}ax+3 & \text{ if }x>0, \\ab & \text{ if }x=0, \\bx+c & \text{ if }x<0.\end{array}\right.$$

If $$f(2)=5$$, $$f(0)=5$$, and $$f(-2)=-10$$, and $$a$$, $$b$$, and $$c$$ are nonnegative integers, then what is $$a+b+c$$?

Apr 26, 2019

#1
+106993
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2)

f(2)=2a+3=5

2a=2

a=1

f(0)=ab=5

1*b=5

b=5

f(-2)=b*-2+c=-10

-2b+c=-10

-2*5+c=-10

-10+c=-10

c=0

a+b+c =       well you can add up single digit numbers I expect.

Apr 26, 2019
#3
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Thank you so much!!! Both the answers were correct.

lolzforlife  Apr 27, 2019
#2
+106993
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1.) Let $$f(x)=\left\lfloor\left(-\frac58\right)^x\right\rfloor$$   be a function that is defined for all values of x in $$[0,\infty)$$ such that f(x) is a real number. How many distinct values exist in the range of f(x)?

The real solutions     (-5/8)^x    are  always going to be between -1 and 1 not inclusive   (when x is positive)

so the floor function can only be  -2, -1  and 0

Hence you can answer the actual question.

Apr 26, 2019