If g(x) = -2x+7, what is the new function defined by h(x) = g(2x^2 +1)
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The domain of a function is the set of the possible values of x, while the range of a function is the set of the resulting values of the functions from the domain.
By inspection it can be seen that the function
f(x) = 4 - 4x has the domain and range as follows:
<span>domain: {0, 1, 3, 5, 6}
range: {-20, -16, -8, 0, 4}
i.e. 4 - 4(0) = 4 - 0 = 4
4 - 4(1) = 4 - 4 = 0
4 - 4(3) = 4 - 12 = -8
4 - 4(5) = 4 - 20 = -16
4 - 4(6) = 4 - 24 = -20
Also, the function
f(x) = 5x - 3 has the domain and range as follows:
</span><span>domain: {-2, -1, 0, 3, 4}
range: {-13, -8, -3, 12, 17}
i.e. 5(-2) - 3 = -10 - 3 = -13
5(-1) - 3 = -5 - 3 = -8
5(0) - 3 = 0 - 3 = -3
5(3) - 3 = 15 - 3 = 12
5(4) - 3 = 20 - 3 = 17
Also, the function
f(x) = -10x has the domain and range as follows:
</span><span>domain: {-4, -2, 0, 2, 4}
range: {-40, -20, 0, 20, 40}
i.e. -10(-4) = 40
-10(-2) = 20
-10(0) = 0
-10(2) = -20
-10(4) = -40
Also, the function
has the domain and range as follows:
</span><span>domain: {-3, -2, -1, 2, 6}
range: {0.5, 0, -1.5, 3, 2}
i.e.
</span>
By inspection it can be seen that the function
f(x) = 4 - 4x has the domain and range as follows:
<span>domain: {0, 1, 3, 5, 6}
range: {-20, -16, -8, 0, 4}
i.e. 4 - 4(0) = 4 - 0 = 4
4 - 4(1) = 4 - 4 = 0
4 - 4(3) = 4 - 12 = -8
4 - 4(5) = 4 - 20 = -16
4 - 4(6) = 4 - 24 = -20
Also, the function
f(x) = 5x - 3 has the domain and range as follows:
</span><span>domain: {-2, -1, 0, 3, 4}
range: {-13, -8, -3, 12, 17}
i.e. 5(-2) - 3 = -10 - 3 = -13
5(-1) - 3 = -5 - 3 = -8
5(0) - 3 = 0 - 3 = -3
5(3) - 3 = 15 - 3 = 12
5(4) - 3 = 20 - 3 = 17
Also, the function
f(x) = -10x has the domain and range as follows:
</span><span>domain: {-4, -2, 0, 2, 4}
range: {-40, -20, 0, 20, 40}
i.e. -10(-4) = 40
-10(-2) = 20
-10(0) = 0
-10(2) = -20
-10(4) = -40
Also, the function
</span><span>domain: {-3, -2, -1, 2, 6}
range: {0.5, 0, -1.5, 3, 2}
i.e.
