Question

Tolong bantuannya kak​

Answer 1

Jawab:

Penjelasan dengan langkah-langkah:

Langkah 1: Menyederhanakan [tex]\(f^{-1}(x)\)[/tex]

[tex]\[ f^{-1}(x) = \frac{2 \cdot \left(\frac{2x + 6}{10}\right) + 6}{10} \]\[ f^{-1}(x) = \frac{\frac{4x + 12}{10} + 6}{10} \]\[ f^{-1}(x) = \frac{\frac{4x + 12 + 60}{10}}{10} \]\[ f^{-1}(x) = \frac{\frac{4x + 72}{10}}{10} \]\[ f^{-1}(x) = \frac{4x + 72}{100} \][/tex]

Langkah 2: Menggantikan [tex]\(x\) dalam \(g(x)\) dengan \(f^{-1}(x)\)[/tex]

[tex]\[ g\left(\frac{4x + 72}{100}\right) = \frac{3 \cdot \left(\frac{4x + 72}{100}\right) + 1}{\left(\frac{4x + 72}{100}\right) - 6} \]\[ g\left(\frac{4x + 72}{100}\right) = \frac{\frac{12x + 216}{100} + 1}{\frac{4x + 72}{100} - 6} \]\[ g\left(\frac{4x + 72}{100}\right) = \frac{\frac{12x + 216 + 100}{100}}{\frac{4x + 72 - 600}{100}} \]\[ g\left(\frac{4x + 72}{100}\right) = \frac{\frac{12x + 316}{100}}{\frac{4x - 528}{100}} \]\[ g\left(\frac{4x + 72}{100}\right) = \frac{12x + 316}{4x - 528} \][/tex]

[tex]( (g \circ f^{-1})(x) = \frac{12x + 316}{4x - 528} \)[/tex]