Respuesta :
Answer:
[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]
Step-by-step explanation:
Given
[tex]f(d) = (0.5 * 10^{-4})^d[/tex]
[tex]g(H+) = -log_{10}(H+)[/tex]
Required
Find the composite function g(f(d))
We have:
[tex]g(H+) = -log_{10}(H+)[/tex]
Substitute f(d) for H+
[tex]g(f(d)) = -log_{10}(f(d))[/tex]
Substitute [tex]f(d) = (0.5 * 10^{-4})^d[/tex]
[tex]g(f(d)) = -log_{10}((0.5 * 10^{-4})^d)[/tex]
Apply law of logarithm
[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]
Hence, the function is:
[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]