SOLUTION: The function f is defined by f(x)= k/x +3, where k is a constant. Find k, if the graph of f passes through the point (3/4 ,0).

Algebra ->  Real-numbers -> SOLUTION: The function f is defined by f(x)= k/x +3, where k is a constant. Find k, if the graph of f passes through the point (3/4 ,0).      Log On


   

Question 1141345: The function f is defined by f(x)= k/x +3, where k is a constant. Find k, if the graph of f passes through the point (3/4 ,0).
Found 2 solutions by Edwin McCravy, josgarithmetic:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
We know that the equation of this graph is y = f(x) = k/x + 3,
and that it passes through the point where the black dot is on the
x-axis which is the point (3/4,0):



But we don't know what number k is in this equation:

f(x) = k/x + 3

So we change f(x) to y:

y = k/x + 3

We replace x by the x coordinate of (3/4, 0) which is 3/4 and
we replace y by the y coordinate of (3/4, 0) which is 0:

0 = k/(3/4) + 3

When we divide by a fraction we invert it and multiply:

0 = k∙(4/3) + 3

0 = (4/3)k + 3

We clear the fraction by multiplying through by the denominator 3

 3∙0 = 3∙(4/3)k + 3∙3
   0 = 4k + 9
  -9 = 4k
-9/4 = k

Edwin

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
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The function f is defined by f(x)= k/x +3, where k is a constant. Find k, if the graph of f passes through the point (3/4 ,0).
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f%28x%29=k%2Fx%2B3

f%28x%29-3=k%2Fx

x%28f%28x%29-3%29=k

k=x%28f%28x%29-3%29
-
Find k for point ( 3/4, 0 ).
k=%283%2F4%29%28-3%29

highlight%28k=-9%2F4%29