Jawaban:
Nomor 3
[tex]g(x) = x - 2[/tex]
Nomor 4
[tex]{(gof)}^{ - 1}(2) = \frac{1}{10} [/tex]
Nomor 5
[tex]({f}^{ - 1} o {g}^{ - 1} )(2) = - 7[/tex]
Penjelasan dengan langkah-langkah:
Nomor 3
[tex] f(x) = 4x + 3 \\ (fog)(x) = 4x - 5 \\ \\ (fog)(x) = f(g(x)) \\ 4x - 5 = 4g(x) + 3 \\ 4g(x) + 3 = 4x - 5 \\ 4g(x) = 4x - 5 - 3 \\ 4g(x) = 4x - 8 \\ g(x) = \frac{4x - 8}{4} \\ g(x) = x - 2[/tex]
Nomor 4
[tex]f(x) = 2x \\ g(x) = 3 - 5x \\ \\ cari \: nilai \:(gof)(x) \\ (gof)(x) = 3 - 5(2x) \\ (gof)(x) = 3 - 10x \\ \\cari \: nilai \: {(gof)}^{ - 1}(x) \\ y = 3 - 10x \\ 10x = 3 - y \\ x = \frac{3 - y}{10} \\ {(gof)}^{ - 1} (x) = \frac{3 - x}{10} \\ \\ {(gof)}^{ - 1}(2) = \frac{3 - 2}{10} \\ {(gof)}^{ - 1}(2) = \frac{1}{10} [/tex]
Nomor 5
[tex]f(x) = x + 3 \\ g(x) = x + 6 \\ \\ cari \: nilai \: {f}^{ - 1} (x) \\ y = x + 3 \\ x = y - 3 \\ {f}^{ - 1} (x) = x - 3 \\ \\ cari \: nilai \: {g}^{ - 1} (x) \\ y = x + 6 \\ x = y - 6 \\ {g}^{ - 1} (x) = x - 6 \\ \\cari \: nilai \: ({f}^{ - 1} o {g}^{ - 1} )(x) \\ ({f}^{ - 1} o {g}^{ - 1} ) (x) = (x - 6) - 3 \\ ({f}^{ - 1} o {g}^{ - 1} )(x) = x - 9 \\ \\ ({f}^{ - 1} o {g}^{ - 1} )(2) = 2 - 9 \\ ({f}^{ - 1} o {g}^{ - 1} )(2) = - 7[/tex]
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