You can
put this solution on YOUR website!First Problem: Find the inverse of f(x)=3x+1
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I'm not exactly sure what you mean by "f:R arrow R". I suspect it has something to do with
mapping. But as to finding the inverse of f(x) ... this is a 4 step process.
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Step 1. Replace f(x) with "y" so that your equation becomes:
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y = 3x + 1
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Step 2. Change the y to x and the x to y so that the equation is then:
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x = 3y + 1
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Step 3. Solve the equation that you got in Step 2 for y.
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Remove the 3y term from the right side by subtracting 3y from both sides. After this subtraction
the equation is then:
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-3y + x = 1
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Remove the x term from the left side by subtracting x from both sides to get:
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-3y = -x + 1
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Divide both sides (all terms) by -3 and you then have:
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Step 4. Replace y with the inverse notation
to get:
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This is the inverse of the function you were given.
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Second problem: If f(x) = x-3 and g(x)=2x+5 find fog and gof
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fog is found by replacing every x that appears in f(x) with the right side of g(x) and then
simplifying the result.
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First the replacement of the x's on the right side of f(x):
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fog = (2x+5) - 3
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then simplify by removing the parentheses and adding +5 and -3 to get:
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fog = 2x + 2
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That's what you are looking for.
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Next find gof. This involves the same process as before. In gof you replace each of the
x's on the right side with the right side of f(x) to get:
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gof = 2(x-3) + 5
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Now simplify starting with doing the multiplication to get:
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gof = 2x - 6 + 5
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then combine the -6 and +5 to get:
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gof = 2x - 1
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And that's the answer.
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Final problem. If f(x) = x^2 + 3x - 5 then f(-2)=
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In f(x) replace every x with -2 and then simplify:
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Then simplify:
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combine to get the answer of f(-2) = -7
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There you go.
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Hope this helps you to understand the basic ideas behind all these operations.
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