f(x)=3x-2, g(x)=3x+2/3, h(x)=x²-2. Evaluate h(3), and g(2). Find x when f(x)=7

Question

This question appeared on my test with a bunch of other Function Notation equations and graphs that confuse me very much. I got 7/45 and have NO CLUE how to solve anything that was on the test. I took great notes, but I don't understand this.

Answer 1

In a previous class you were probably asked to solve for x, and as well to solve for two symbols or more.  For instance, the class y-intercept equation form:

 

  y = m*x + b

 

where you were given some of them and asked to find others.  Sometimes given a point in an x,y grid, but this doesn't involve a grid, but the symbolic formulas.  So, for instance, you may have been given:

 

  y = 3x - 2

 

solve this when y is 7.  That would yield:

 

  7 = 3x - 2

    (isolate x, so get rid of the -2 by doing the opposite: add 2 to both sides)

  9 = 3x

    (isolate x again, so divide by 3... on both sides)

  3 = x

 

This is similar, except instead of y you're being given f(x).  f(x) can be said as "f of x" or "function f depends upon x".  So given say:

 

  f(x) = 3x - 2

 

if we're told f(x)=7 then we replace f(x) with 7, hence:

 

  7 = 3x - 2

 

And you get x = 3 as per above.  Now, there is a twist when we are not given "f(x)=7" but just say "f(1)".  In that case, leave f(x) alone but in the specific form (f(1)) and since f depends upon x, we use 1 as x, since in this case f depends upon 1.  So, IOWs:

 

  f(1) = 3x - 2 --> substitute 1 for x, so:

  f(1) = 3(1) - 2 --> now just solve:

  f(1) = 3 - 2 = 1 --> therefore:

  f(1) = 1

 

So given:

 

  g(x) = 3x + 2/3 AND g(2)

 

we get:

 

  g(2) = 3(2) + 2/3

  g(2) = 6 + 2/3

  g(2) = 6 2/3

 

In the last, we have:

 

  h(x)=x²-2 AND h(3)

 

So substituting for x we get:

 

  h(3) =3² - 2

  h(3) = 9 - 2

  h(3) = 7

 

- Greg, from Queens, New York City

Answer 2

f(x)=3x-2

f(x)=7

7=3x-2

7+2=3x

9=3x

x=3

g(x)=3x+ 2/3

g(2)=3(2)+ 2/3

      =6 2/3

h(x)=x²-2

h(3)=3²-2

      =9-2

      =7