Function assign value from one set to another. The value of f(5), if f(1) = 3.2 and f(x+1) = Five-halves(f(x)) is 125.
A function assigns the value of each element of one set to the other specific element of another set.
As it is given the value of the function f(1) is 3.2, while the value of f(x+1) is [tex]f(x+1) = \dfrac{5}{2}[f(x)][/tex], therefore, in order to find the value of f(5), we need to calculate the value of f(4).
f(2)
[tex]f(x+1) = \dfrac{5}{2}[f(x)]\\\\f(2)=f(1+1) = \dfrac{5}{2}[f(1)]\\\\f(2) = 2.5 \times 3.2\\\\f(2) = 8[/tex]
f(3)
[tex]f(x+1) = \dfrac{5}{2}[f(x)]\\\\f(3)=f(2+1) = \dfrac{5}{2}[f(2)]\\\\f(3) = 2.5 \times 8\\\\f(3) = 20[/tex]
f(4)
[tex]f(x+1) = \dfrac{5}{2}[f(x)]\\\\f(4)=f(3+1) = \dfrac{5}{2}[f(3)]\\\\f(4) = 2.5 \times 20\\\\f(4) = 50[/tex]
f(5)
[tex]f(x+1) = \dfrac{5}{2}[f(x)]\\\\f(5)=f(4+1) = \dfrac{5}{2}[f(4)]\\\\f(5) = 2.5 \times 50\\\\f(5) = 125[/tex]
Hence, the value of f(5), if f(1) = 3. 2 and f(x+1) = Five-halves(f(x)) is 125.
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