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Define the following: i- The function ii- Function range. If f(x) = x²−3, g(x) = 3x +1 Find: i- (f)(2) ii- g(2) iii- (2)
Mathematics
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6 stepsQuestion One:
A-(1) Define the following:
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i- The function A function is a relation between a set of inputs (called the domain) and a set of permissible outputs (called the codomain) with the property that each input is related to exactly one output.
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ii- Function range The range of a function is the set of all actual output values that the function produces for the given inputs in its domain.
A-(2) If , Find:
- i-
Substitute into the function .
$$ f(2) = (2)^2 - 3 $$Calculate the value.
$$ f(2) = 4 - 3 $$ $$ f(2) = \boxed{1} $$- ii-
Substitute into the function .
$$ g(2) = 3(2) + 1 $$Calculate the value.
$$ g(2) = 6 + 1 $$ $$ g(2) = \boxed{7} $$- iii-
This expression means .
Use the values calculated in parts i and ii.
Substitute the values of and .
$$ \frac{f}{g}(2) = \frac{1}{7} $$ $$ \frac{f}{g}(2) = \boxed{\frac{1}{7}} $$
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