Bantuannya guyss

<p><strong>Nomor 1</strong></p><p>Diketahui f(x) = 2x + 1 dan g(x) = 6x - 7.</p><p>Terlebih dahulu dicari invers masing-masing fungsi:</p><p>y = 2x + 1 =&gt; 2x = y - 1 =&gt; x = y - 1 / 2</p><p>f^-1(x) = x - 1 / 2</p><p>y = 6x - 7 =&gt; 6x = y + 7 =&gt; x = y + 7 / 6</p><p>g^-1(x) = x + 7 / 6</p><p><strong>a. Menentukan (g </strong>o<strong> f)^-1(x)</strong></p><p>Cari (g o f)(x) terlebih dahulu:</p><p>(g o f)(x) = g(f(x)) = 6(2x + 1) - 7 = 12x + 6 - 7 = 12x - 1</p><p>Tentukan inversnya:</p><p>y = 12x - 1 =&gt; 12x = y + 1 =&gt; x = y + 1 / 12</p><p>(g o f)^-1(x) = x + 1 / 12</p><p><strong>b. Menentukan (g^-1 </strong>o<strong> f^-1)(x)</strong></p><p>Sesuai definisi komposisi invers:</p><p>(g^-1 o f^-1)(x) = g^-1(f^-1(x)) = g^-1(x - 1 / &nbsp;2)</p><p>= x - 1 / 2 + 7 / 6 = x - 1 + 14 / 2 /6 = x + 13 / 12</p><p><strong>c. Menentukan (f^-1 </strong>o<strong> g^-1)(x)</strong></p><p>Sesuai sifat fungsi invers, (f^-1 o g^-1)(x) = (g o f)^-1(x):</p><p>(f^-1 o g^-1)(x) = f^-1(g^-1(x)) = f^-1(x + 7 / 6)</p><p>= x + 7 / 6 - 1 / 2 &nbsp;= x + 7 - 6 / 6 / 2 = x + 1 / 12</p><p><strong>d. Menentukan (f </strong>o<strong> g)^-1(5)</strong></p><p>Cari fungsi (f o g)(x):</p><p>(f o g)(x) = f(g(x)) = 2(6x - 7) + 1 = 12x - 14 + 1 = 12x - 13</p><p>Karena (f o g)^-1(5) = k &lt;=&gt; (f o g)(k) = 5:</p><p>12k - 13 = 5</p><p>12k = 18</p><p>k = 18/12 = 3/2</p><p>(f o g)^-1(5) = 3/2</p><p>&nbsp;</p><p><strong>Nomor 2</strong></p><p>Diketahui f(x) = 1/2 x - 3 dan (g o f)^-1(x) = x + 2.</p><p>Tentukan (g o f)(x) dengan mencari invers dari (g o f)^-1(x):</p><p>y = x + 2 =&gt; x = y - 2</p><p>(g o f)(x) = x - 2</p><p>Gunakan persamaan komposisi:</p><p>g(f(x)) = x - 2</p><p>g(1/2 x - 3) = x - 2</p><p>Misalkan u = 1/2 x - 3:</p><p>1/2 x = u + 3 =&gt; x = 2u + 6</p><p>Substitusikan nilai x ke dalam persamaan:</p><p>g(u) = (2u + 6) - 2</p><p>g(u) = 2u + 4</p><p>Jadi, <strong>g(x) = 2x + 4</strong>.</p><p>&nbsp;</p><p><strong>Nomor 3</strong></p><p>Diketahui f(x) = 3 + 2x, g(x) = 2 + x, dan h(x) = 2x. Ditanyakan nilai x jika&nbsp;</p><p>(f o g o h)^-1(x) = -1.</p><p>Sesuai sifat fungsi invers:</p><p>(f o g o h)^-1(x) = -1 &lt;=&gt; (f o g o h)(-1) = x</p><p>Hitung secara berurutan dari dalam ke luar:</p><p>h(-1) = 2(-1) = -2</p><p>g(h(-1)) = g(-2) = 2 + (-2) = 0</p><p>f(g(h(-1))) = f(0) = 3 + 2(0) = 3</p><p>Jadi, nilai <strong>x = 3</strong>.</p>